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Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling

Published online by Cambridge University Press:  17 April 2015

Filip Lindskog  and
Alexander J. McNeil
Filip Lindskog
Affiliation:
Risklab, Federal Institute of Technology, ETH Zentrum, CH-8092 Zurich, Tel.: +41 1 632 67 41, Tel.: +41 1 632 10 85, lindskog@math.ethz.ch
Alexander J. McNeil
Affiliation:
Department of Mathematics, Federal Institute of Technology, ETH Zentrum, CH-8092 Zurich, Tel.: +41 1 632 61 62, Tel.: +41 1 632 15 23, mcneil@math.ethz.ch
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Abstract

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The idea of using common Poisson shock processes to model dependent event frequencies is well known in the reliability literature. In this paper we examine these models in the context of insurance loss modelling and credit risk modelling. To do this we set up a very general common shock framework for losses of a number of different types that allows for both dependence in loss frequencies across types and dependence in loss severities. Our aims are threefold: to demonstrate that the common shock model is a very natural way of approaching the modelling of dependent losses in an insurance or risk management context; to provide a summary of some analytical results concerning the nature of the dependence implied by the common shock specification; to examine the aggregate loss distribution that results from the model and its sensitivity to the specification of the model parameters.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 2 , November 2003 , pp. 209 - 238
Copyright
Copyright © ASTIN Bulletin 2003

Footnotes

*

Research of the first author was supported by Credit Suisse Group, Swiss Re and UBS AG through RiskLab, Switzerland. We thank in particular Nicole Bäuerle for commenting on an earlier version of this paper.

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